Reddit's comment ranking

confidence.py

# http://amix.dk/blog/post/19588?source=google
from math import sqrt

def _confidence(ups, downs):
    n = ups + downs

    if n == 0:
        return 0

    z = 1.0 #1.0 = 85%, 1.6 = 95%
    phat = float(ups) / n
    return sqrt(phat+z*z/(2*n)-z*((phat*(1-phat)+z*z/(4*n))/n))/(1+z*z/n)

def confidence(ups, downs):
    if ups + downs == 0:
        return 0
    else:
        return _confidence(ups, downs)

This doesn't match the comment ranking as described in this 2009 post on the Reddit blog: http://blog.reddit.com/2009/10/reddits-new-comment-sorting-system.html or specifically in this link from that post: http://www.evanmiller.org/how-not-to-sort-by-average-rating.html

In particular, instead of wrapping the whole numerator in sqrt(), you want to wrap only the expression (phat_(1-phat)+z_z/(4*n))/n. This is a major difference in the formula.

Also, z = 1.0 corresponds to an 84% confidence interval, not 85%; but in any case the gist is described as "Reddit's comment ranking", and at least as of that 2009 blog post Reddit used a 95% confidence interval. Do you know that that's changed? If not, it'd be better to write z = 1.64, which gives a 95% confidence interval.

OK, here's the actual Reddit comment ranking, according to their own open-sourced code:
https://github.com/reddit/reddit/blob/master/r2/r2/lib/db/_sorts.pyx#L40

It puts the sqrt() in the place I described, and then their z-value turns out to be this:

 z = 1.281551565545 # 80% confidence